Polar to Rectangular Complex Number Converter

Effortlessly convert complex numbers from polar form (r, θ) to rectangular form (a + bi). Visualize the conversion on the complex plane.

Input Values

Enter the magnitude and argument of the complex number in polar form.

Magnitude (r):

| r

Argument (θ) in Radians:

rad |

Result

Rectangular Form (a + bi):

Real Part (a): , Imaginary Part (b):

Visualization

Understanding Polar to Rectangular Form Conversion

In mathematics, a complex number can be represented in polar form using its magnitude (r) and argument (θ), or in rectangular form as a + bi, where 'a' is the real part and 'b' is the imaginary part. This tool converts from polar form to rectangular form using the formulas:

Real part (a) = r * cos(θ)
Imaginary part (b) = r * sin(θ)

Magnitude (r) is the distance from the origin to the complex number in the complex plane, and argument (θ) is the angle between the positive real axis and the line connecting the origin to the complex number, measured in radians. This conversion is useful in various fields like physics and engineering for simplifying calculations involving complex numbers.

Learn more about complex numbers on Wikipedia.